In algebraic geometry, local uniformization is a weak form of resolution of singularities, stating roughly that a variety can be desingularized near any valuation, or in other words that the Zariski–Riemann space of the variety is in some sense nonsingular. Local uniformization was introduced by Zariski , who separated out the problem of resolving the singularities of a variety into the problem of local uniformization and the problem of combining the local uniformizations into a global desingularization.